Elliptic curve isogeny class with LMFDB label 7488.e (Cremona label 7488cd)

• Label: 7488.e
• Number of curves: $2$
• Conductor: $7488$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 7488.e have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 4 T + 5 T^{2}\)	1.5.e
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 7488.e do not have complex multiplication.

Modular form 7488.2.a.e

Isogeny matrix

The \((i,j)\)-th entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 7488.e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
7488.e1	7488cd2	\([0, 0, 0, -2172, 35440]\)	\(94875856/9477\)	\(113192681472\)	\([2]\)	\(12288\)	\(0.85741\)
7488.e2	7488cd1	\([0, 0, 0, 168, 2680]\)	\(702464/4563\)	\(-3406261248\)	\([2]\)	\(6144\)	\(0.51084\)	\(\Gamma_0(N)\)-optimal